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DOI: 10.4230/LIPIcs.MFCS.2019.70

Acceptance Ambiguity for Quantum Automata

Authors: Paul C. Bell and Mika Hirvensalo

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract

We consider notions of freeness and ambiguity for the acceptance probability of Moore-Crutchfield Measure Once Quantum Finite Automata (MO-QFA). We study the distribution of acceptance probabilities of such MO-QFA, which is partly motivated by similar freeness problems for matrix semigroups and other computational models. We show that determining if the acceptance probabilities of all possible input words are unique is undecidable for 32 state MO-QFA, even when all unitary matrices and the projection matrix are rational and the initial configuration is defined over real algebraic numbers. We utilize properties of the skew field of quaternions, free rotation groups, representations of tuples of rationals as a linear sum of radicals and a reduction of the mixed modification Post’s correspondence problem.

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Paul C. Bell and Mika Hirvensalo. Acceptance Ambiguity for Quantum Automata. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 70:1-70:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bell_et_al:LIPIcs.MFCS.2019.70,
  author =	{Bell, Paul C. and Hirvensalo, Mika},
  title =	{{Acceptance Ambiguity for Quantum Automata}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{70:1--70:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.70},
  URN =		{urn:nbn:de:0030-drops-110149},
  doi =		{10.4230/LIPIcs.MFCS.2019.70},
  annote =	{Keywords: Quantum finite automata, matrix freeness, undecidability, Post’s correspondence problem, quaternions}
}

Document

DOI: 10.4230/LIPIcs.ECOOP.2017.19

Proactive Synthesis of Recursive Tree-to-String Functions from Examples

Authors: Mikaël Mayer, Jad Hamza, and Viktor Kuncak

Published in: LIPIcs, Volume 74, 31st European Conference on Object-Oriented Programming (ECOOP 2017)

Abstract

Synthesis from examples enables non-expert users to generate programs by specifying examples of their behavior. A domain-specific form of such synthesis has been recently deployed in a widely used spreadsheet software product. In this paper we contribute to foundations of such techniques and present a complete algorithm for synthesis of a class of recursive functions defined by structural recursion over a given algebraic data type definition. The functions we consider map an algebraic data type to a string; they are useful for, e.g., pretty printing and serialization of programs and data. We formalize our problem as learning deterministic sequential top-down tree-to-string transducers with a single state (1STS). The first problem we consider is learning a tree-to-string transducer from any set of input/output examples provided by the user. We show that, given a set of input/output examples, checking whether there exists a 1STS consistent with these examples is NP-complete in general. In contrast, the problem can be solved in polynomial time under a (practically useful) closure condition that each subtree of a tree in the input/output example set is also part of the input/output examples. Because coming up with relevant input/output examples may be difficult for the user while creating hard constraint problems for the synthesizer, we also study a more automated active learning scenario in which the algorithm chooses the inputs for which the user provides the outputs. Our algorithm asks a worst-case linear number of queries as a function of the size of the algebraic data type definition to determine a unique transducer. To construct our algorithms we present two new results on formal languages. First, we define a class of word equations, called sequential word equations, for which we prove that satisfiability can be solved in deterministic polynomial time. This is in contrast to the general word equations for which the best known complexity upper bound is in linear space. Second, we close a long-standing open problem about the asymptotic size of test sets for context-free languages. A test set of a language of words L is a subset T of L such that any two word homomorphisms equivalent on T are also equivalent on L. We prove that it is possible to build test sets of cubic size for context-free languages, matching for the first time the lower bound found 20 years ago.

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Mikaël Mayer, Jad Hamza, and Viktor Kuncak. Proactive Synthesis of Recursive Tree-to-String Functions from Examples. In 31st European Conference on Object-Oriented Programming (ECOOP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 74, pp. 19:1-19:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{mayer_et_al:LIPIcs.ECOOP.2017.19,
  author =	{Mayer, Mika\"{e}l and Hamza, Jad and Kuncak, Viktor},
  title =	{{Proactive Synthesis of Recursive Tree-to-String Functions from Examples}},
  booktitle =	{31st European Conference on Object-Oriented Programming (ECOOP 2017)},
  pages =	{19:1--19:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-035-4},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{74},
  editor =	{M\"{u}ller, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2017.19},
  URN =		{urn:nbn:de:0030-drops-72575},
  doi =		{10.4230/LIPIcs.ECOOP.2017.19},
  annote =	{Keywords: programming by example, active learning, program synthesis}
}

Document

DOI: 10.4230/DagSemProc.08391.3

08391 Group Summary – Mining for Social Serendipity

Authors: Alexandre Passant, Ian Mulvany, Peter Mika, Nicolas Maisonneuve, Alexander Löser, Ciro Cattuto, Christian Bizer, Christian Bauckhage, and Harith Alani

Published in: Dagstuhl Seminar Proceedings, Volume 8391, Social Web Communities (2008)

Abstract

A common social problem at an event in which people do not personally know all of the other participants is the natural tendency for cliques to form and for discussions to mainly happen between people who already know each other. This limits the possibility for people to make interesting new acquaintances and acts as a retarding force in the creation of new links in the social web. Encouraging users to socialize with people they don't know by revealing to them hidden surprising links could help to improve the diversity of interactions at an event. The goal of this paper is to propose a method for detecting extit{"surprising"} relationships between people attending an event. By extit{"surprising"} relationship we mean those relationships that are not known a-priori, and that imply shared information not directly related with the local context of the event (location, interests, contacts) at which the meeting takes place. To demonstrate and test our concept we used the Flickr community. We focused on a community of users associated with a social event (a computer science conference) and represented in Flickr by means of a photo pool devoted to the event. We use Flickr metadata (tags) to mine for user similarity not related to the context of the event, as represented in the corresponding Flickr group. For example, we look for two group members who have been in the same highly specific place (identified by means of geo-tagged photos), but are not friends of each other and share no other common interests or, social neighborhood.

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Alexandre Passant, Ian Mulvany, Peter Mika, Nicolas Maisonneuve, Alexander Löser, Ciro Cattuto, Christian Bizer, Christian Bauckhage, and Harith Alani. 08391 Group Summary – Mining for Social Serendipity. In Social Web Communities. Dagstuhl Seminar Proceedings, Volume 8391, pp. 1-11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{passant_et_al:DagSemProc.08391.3,
  author =	{Passant, Alexandre and Mulvany, Ian and Mika, Peter and Maisonneuve, Nicolas and L\"{o}ser, Alexander and Cattuto, Ciro and Bizer, Christian and Bauckhage, Christian and Alani, Harith},
  title =	{{08391 Group Summary – Mining for Social Serendipity}},
  booktitle =	{Social Web Communities},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8391},
  editor =	{Harith Alani and Steffen Staab and Gerd Stumme},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08391.3},
  URN =		{urn:nbn:de:0030-drops-17910},
  doi =		{10.4230/DagSemProc.08391.3},
  annote =	{Keywords: Serendipity, online activity, context, ubiquitous computing}
}

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Acceptance Ambiguity for Quantum Automata

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Proactive Synthesis of Recursive Tree-to-String Functions from Examples

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08391 Group Summary – Mining for Social Serendipity

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